Un of Tenn | Math Department

Seminars and Colloquiums
for the week of February 1, 2010

Speaker:

Professor Jim Conant, Monday
Professor Gabriel Tucci, Bell Labs, Monday
Professor Mohammud Foondun, Loughborough University, Tuesday
Mr. Chad Kilpatrick, Wednesday
Professor Ken Stephenson, Wednesday
Professor Judy Day, Postdoctoral Research Fellow, Mathematical Biosciences Institute (NIMBioS candidate), Thursday
Professor Jamie Sethian, UC Berkeley, Thursday
Professor Jerzy Dydak, Friday

Monday, February 1

TOPOLOGY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: EST 209
SPEAKER: Professor Jim Conant
TITLE: “Khovanov Homology”
ABSTRACT: In this talk, we will discuss Khovanov's fascinating generalization of the Jones polynomial. This theory assigns a combinatorially defined chain complex to every link diagram, in such a way that the homology of this chain complex is a link invariant. Moreover, the graded Euler characteristic is nothing other than the Jones polynomial. I will try to make this talk accessible to newcomers.

COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: HBB 102
SPEAKER: Professor Gabriel Tucci, Bell Labs
TITLE: “Random Matrices and their applications to information theory and multivariate statistics”
ABSTRACT: Random matrix theory is an important and active research area in mathematics. Nowadays, random matrices find applications in fields as diverse as the Riemann conjecture, physics, chaotic systems, multivariate statistics, wireless communications, signal processing, compressed sensing and information theory.

In the last decades, a considerable amount of work on the fundamental limits of communication channels makes use of results in random matrix theory. It is for this reason that it is often necessary to compute averages over certain matrix ensembles. A typical example is the capacity of the single user MIMO communication channel. Another important area where averages over random matrices appear is multivariate statistics. For instance, the estimation of a covariance matrix from insufficient data is one of the most common problems in multivariate statistics. More specifically, if we have a set of $n$ independent identically distributed measurements of an $m$--dimensional random vector with $n<m$, the maximum--likelihood estimate is the sample covariance matrix, but here this estimate is singular and therefore fundamentally bad. In this talk we will discuss two concrete projects done at Bell Labs where we address these problems using random matrices techniques.

Tuesday, February 2

COLLOQUIUM
TIME: 3:35-4:25 p.m.
ROOM: HBB102
SPEAKER: Professor Mohammud Foondun, Loughborough University
TITLE: “Levy processes and Stochastic partial differential equations”
ABSTRACT: It is known that some stochastic partial differential equations suffer from `the curse of dimensionality'. That is, they do not possess random-field solutions in spatial dimension d greater than or equal to 2. In this talk, I will sketch a proof of this phenomenon and provide an alternative explanation based on a property of Levy processes, called local times. This connection between local times of Levy processes and solutions to stochastic partial differential equations also goes beyond existence and uniqueness properties. In fact, a lot of properties of the solutions can be deduced from the properties of local times.

Wednesday, February 3

COARSE GEOMETRY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: Estabrook Hall (EST) 209
SPEAKER: Mr. Chad Kilpatrick
TITLE: “Intro. to C*-Algebras: The Uniform Roe Algebra
and the Reduced Group C*-algebra
ABSTRACT: In this talk, I introduce basic notions of C*-algebras, defining the uniform Roe algebra, Cu*(X) of a bonded geometry space X, and the reduced group C*-algebra, Cr*(G) of a countable discrete group G. I then characterize Cr*(G) and Cu*(X) as C*-subalgebras of B(l2(G)) and B(l2(X)) generated by certain classes of convolution operators on l2(G) and l2(X), resp. When X is the underlying metric space of G, the aforementioned characterization shows that Cr*(G) is a C*-subalgebra of Cu*(X). In this talk, I closely follow Ch. 4: "Connections with C*-Algebras” from Rufus Willet’s Some Notes on Property A.

ANALYSIS SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: HBB132
SPEAKER: Professor Ken Stephenson
TITLE: “Come and watch me circle pack AGAIN!”
ABSTRACT: In the first talk I illustrated some experiments with my software package, CirclePack, mostly related to complex function theory. In the second talk I'll demonstrate some alternate experimental and game settings. Mainly, however, I plan to discuss issues of programming and computation, encounters with big science, experimentalist frustrations --- and in general, about mathematics as an enterprise.

Thursday, February 4

COLLOQUIUM
TIME: 10:00 a.m.
ROOM: Ferris Hall 510
SPEAKER: Professor Judy Day, Postdoctoral Research Fellow, Mathematical Biosciences Institute (NIMBioS candidate)
TITLE: “Modeling the immune rheostat of macrophages in the lung in response to infection”
ABSTRACT: In the lung, alternatively activated macrophages (AAM) form the first line of defense against microbial infection. Due to the highly regulated nature of AAM, the lung can be considered as an immunosuppressive organ for respiratory pathogens. However, as infection progresses in the lung, another population of macrophages, known as classically activated macrophages (CAM) enters; these cells are typically activated by cytokines IFN-gamma and TNF-alpha. CAM are far more effective than AAM in clearing the microbial load, producing pro-inflammatory cytokines and anti-microbial defense mechanisms necessary to mount an adequate immune response. The present work is concerned with determining the first time when the population of CAM becomes more dominant than the population of AAM. This proposed "switching time" is explored in the context of Mycobacterium tuberculosis (MTb) infection. During the course of a simulated MTb infection, the model predicts a switching time of 50 days (~7 weeks), which agrees well with the average time between initial exposure and a positive MTb skin test (6-12 weeks). The simulations show that the AAM not only ineffectively deal with the bacteria, but also prevent early recruitment of necessary effector cells, positioning their bacterial opponent at an unfair advantage. This immune battlefield may also negatively influence vaccine strategies in the lung microenvironment. Hence, if the switching time could be altered to occur earlier in the response, then, theoretically, tuberculosis therapies along with a more robust immune system may clear the disease more effectively, since a reduced switching time may imply reduced peak bacterial loads. Treatment simulations involving IFN-gamma therapy reduce the switching time to 34 days and reduce peak and residual bacterial loads. Generally speaking, our results suggest that a reduction in the switching time correlates with lower peak and residual bacterial loads, and therapeutic strategies should aim to reduce bacterial numbers while not reducing the signaling to -downstream mediators.

COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: HBB102
SPEAKER: Professor Jamie Sethian, UC Berkeley
TITLE: “Advances in Advancing Interfaces: Efficient Algorithms for Inkjet Plotters, Coating Rollers, Semiconductors, and Medical Scanners”
ABSTRACT: Propagating interfaces occur in a wide variety of settings, and include ocean waves, burning flames, and material boundaries. Less obvious boundaries are equally important, and include iso-intensity contours in images, handwritten characters, and shapes against boundaries. In addition, some static problems can be recast as advancing fronts, including robotic navigation and finding shortest paths on contorted surfaces.

One way to frame moving interfaces is to recast them as solutions to fixed domain Eulerian partial differential equations, and this has led to a collection of PDE-based techniques, including level set methods, fast marching methods, and ordered upwind methods. These techniques easily accommodate merging boundaries and the delicate 3D physics of interface motion. In many settings, they been proven valuable.

In this talk, we will focus on industrial applications of these techniques. The goal is to give an overview of some of the computational complexities involved in optimizing ink jet plotters, micro fluidics, simulating semiconductor manufacturing, and extracting anatomical structures through image segmentation in medical scanners.

Friday, February 5

TOPOLOGY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: Estabrook Hall (EST) 209
SPEAKER: Professor Jerzy Dydak
TITLE: “Introduction to CAT(0) spaces”
ABSTRACT: This is the beginning of a series of talks on two classical methods in the study of infinite groups:
1. Rigidity theory, which studies groups that are nicely embedded in Lie groups.
2. Actions on non-positively curved manifolds.
A modern approach unifies and generalizes these into one framework: group actions on metric spaces of non-positive curvature. We will start with the concept of a CAT(0) space, an abstraction of the fundamental notion of non-positive curvature from Riemannian manifolds to general metric spaces, and it will be of interest to anyone who has studied negatively curved manifolds. We will apply this to the study of infinite groups, and prove celebrated rigidity results which are among the major highlights of modern group theory.

Here is the plan for this semester and beyond:
• Generalizing the concept of curvature to more general metric spaces and the axioms.
• Examples: simply connected manifolds of non-positive curvature, symmetric spaces, buildings.
• Basic notions: projections, center of mass, Bruhat-Tits fixed point theorem.
• Applications: Hopf-Rinow theorem; Cartan-Hadamard theorem.
• Boundaries of spaces.
• Local criteria for non positive curvature and Gromov’s theorem on symplicial complexes.
• Group actions and splitting theorems.
• Monod’s generalization of Margulis superrigidity for lattices in products.
• From rigidity to arithmeticity.
• Caprace-Monod’s generalization of Borel-Density theorem for lattices in CAT(0) spaces.

If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.

If you have questions, or a date you would like to confirm, please contact Dr. Steve Wise.

Week of: